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On the Approximability of Orthogonal Order Preserving Layout Adjustment

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Algorithms and Data Structures (WADS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9214))

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Abstract

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e. maintains the sorted ordering of the rectangle centers along both x-axis and y-axis with respect to the initial placement. This problem is known as Layout Adjustment for Disjoint Rectangles (LADR). It was known that LADR is \(\mathbb {NP}\)-hard, but only heuristics were known for it. We show that a certain decision version of LADR is \(\mathbb {APX}\)-hard, and give a constant factor approximation for LADR.

This material is based upon work supported by the National Science Foundation under Grant CCF-1318996.

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References

  1. Adamaszek, A., Wiese, A.: A quasi-ptas for the two-dimensional geometric knapsack problem. In: SODA, pp. 1491–1505 (2015)

    Google Scholar 

  2. Agarwal, P.K., van Kreveld, M.J., Suri, S.: Label placement by maximum independent set in rectangles. Comput. Geom. 11(3–4), 209–218 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brandes, U., Pampel, B.: Orthogonal-ordering constraints are tough. J. Graph Algorithms Appl. 17(1), 1–10 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bridgeman, S.S., Tamassia, R.: Difference metrics for interactive orthogonal graph drawing algorithms. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 57–71. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Bridgeman, S., Tamassia, R.: A user study in similarity measures for graph drawing. J. Graph Algorithms Appl. 6(3), 225–254 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eades, P., Lai, W., Misue, K., Sugiyama, K.: Preserving the mental map of a diagram. International Institute for Advanced Study of Social Information Science, Fujitsu Limited (1991)

    Google Scholar 

  7. Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634–652 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gaur, D.R., Ibaraki, T., Krishnamurti, R.: Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem. J. Algorithms 43(1), 138–152 (2002)

    Article  MathSciNet  Google Scholar 

  9. Harren, R., Jansen, K., Prädel, L., van Stee, R.: A (5/3 + \(\varepsilon \))-approximation for strip packing. Comput. Geom. 47(2), 248–267 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Harren, R., van Stee, R.: Improved absolute approximation ratios for two-dimensional packing problems. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) Approximation, Randomization, and Combinatorial Optimization. LNCS, vol. 5687, pp. 177–189. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Hassin, R., Megiddo, N.: Approximation algorithms for hitting objects with straight lines. Discrete Appl. Math. 30(1), 29–42 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hayashi, K., Inoue, M., Masuzawa, T., Fujiwara, H.: A layout adjustment problem for disjoint rectangles preserving orthogonal order. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 183–197. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Herman, I., Melançon, G., Marshall, M.S.: Graph visualization and navigation in information visualization: A survey. IEEE Transactions on Visualization and Computer Graphics 6(1), 24–43 (2000)

    Article  Google Scholar 

  14. Huang, X., Lai, W., Sajeev, A., Gao, J.: A new algorithm for removing node overlapping in graph visualization. Information Sciences 177(14), 2821–2844 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. van Kreveld, M.J., Strijk, T., Wolff, A.: Point labeling with sliding labels. Comput. Geom. 13(1), 21–47 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, W., Eades, P., Nikolov, N.S.: Using spring algorithms to remove node overlapping. APVIS. CRPIT 45, 131–140 (2005)

    Google Scholar 

  17. Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141(2), 241–252 (2002)

    Article  MathSciNet  Google Scholar 

  18. Misue, K., Eades, P., Lai, W., Sugiyama, K.: Layout adjustment and the mental map. Journal of visual languages and computing 6(2), 183–210 (1995)

    Article  Google Scholar 

  19. Schiermeyer, I.: Reverse-fit: A 2-optimal algorithm for packing rectangles. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 290–299. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  20. Steinberg, A.: A strip-packing algorithm with absolute performance bound 2. SIAM J. Comput. 26(2), 401–409 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  21. Storey, M.A.D., Müller, H.A.: Graph layout adjustment strategies. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 487–499. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Iowa, Iowa City, USA

    Sayan Bandyapadhyay, Santanu Bhowmick & Kasturi Varadarajan

Authors
  1. Sayan Bandyapadhyay
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  2. Santanu Bhowmick
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  3. Kasturi Varadarajan
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Corresponding author

Correspondence to Kasturi Varadarajan .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Carleton University, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. University of Victoria, Victoria, Canada

    Ulrike Stege

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Bandyapadhyay, S., Bhowmick, S., Varadarajan, K. (2015). On the Approximability of Orthogonal Order Preserving Layout Adjustment. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-21840-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21839-7

  • Online ISBN: 978-3-319-21840-3

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